Nothing in the rules seems to say that you can't so I think its perfectly fine! Just don't make it obnoxiously loud I guess.
i would highly recommend against it. there is nothing officially banning it. however sound is important for verification purposes and if we cannot verify the audio we may have to reject the run if say the video drops frames (looks like splicing ect) or other unforeseen issues arise. i would even go as far to say its an "unofficial rule" to have game audio with the run itself. nothing is stopping you from doing a local recording with just game audio and have music on stream.
Yeah, this is one of those cases where it should just be taken as an implicit rule that applies to speedruns in general. Saying "It's not banned in the rules, so it's ok" is weak reasoning when you can substitute it for anything else.
"Using passwords isn't banned in the rules, so it's ok!" "Using Gameshark codes isn't banned in the rules, so it's ok!"
At some point it does just need to be common sense what is and isn't permissible.
For the longest time, the individual level leaderboards didn't distinguish weither or not you performed them Glitched or Glitchless. So for a majority of levels, Glitched always came out on top if you wanted to achieve top rankings. But now levels will be separated depending on play-style, with a co
